If $0\to E\to F\xrightarrow{\phi}\mathbb{A}^1_X\to 0$ is an exact sequence of bundles over the scheme $X$, then it is known that if $s\colon X\to \mathbb{A}^1_X$ is the constant section sending everything to $1$, then $\phi^{-1}(s(X))$ is an $E$-torsor.
With $E$ still a vector bundle over $X$, if you have any $E$-torsor $P$, can we always find some exact sequence such that $P$ is isomorphic to $\phi^{-1}(s(X))$ for some exact sequence as above?